LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening

TL;DR

LGDC introduces a hybrid graph generation framework that combines spectrum-preserving coarsening with latent discrete diffusion. By operating diffusion in a compact latent space and performing a single expansion–refinement decoding, LGDC achieves strong global coherence and fine-grained local fidelity while reducing computational cost compared to pure diffusion or autoregressive methods. Empirical results on Tree, Planar, and Community-20 graphs show LGDC matches autoregressive performance on locally structured data and diffusion performance on globally structured data, validating the local-global trade-off in a single pipeline. The approach offers practical efficiency and scalability advantages for structure-aware graph generation across domains, with potential extensions to richer attributes and larger heterogeneous graphs.

Abstract

Graph generation is a critical task across scientific domains. Existing methods fall broadly into two categories: autoregressive models, which iteratively expand graphs, and one-shot models, such as diffusion, which generate the full graph at once. In this work, we provide an analysis of these two paradigms and reveal a key trade-off: autoregressive models stand out in capturing fine-grained local structures, such as degree and clustering properties, whereas one-shot models excel at modeling global patterns, such as spectral distributions. Building on this, we propose LGDC (latent graph diffusion via spectrum-preserving coarsening), a hybrid framework that combines strengths of both approaches. LGDC employs a spectrum-preserving coarsening-decoarsening to bidirectionally map between graphs and a latent space, where diffusion efficiently generates latent graphs before expansion restores detail. This design captures both local and global properties with improved efficiency. Empirically, LGDC matches autoregressive models on locally structured datasets (Tree) and diffusion models on globally structured ones (Planar, Community-20), validating the benefits of hybrid generation.

Figures (4)

• Figure 1: Two categories of graph generation methods.
• Figure 2: The architecture of LGDC framework (Latent Graph Diffusion via Coarsening)
• Figure 3: The time complexity of One-shot graph generation. Given the number of nodes $n$, dimension size $d$, number of layers $L$, and number of samples $S$, the overall model complexity for training is given as $O(S\cdot L\cdot (n^2\cdot d^2+n^2\cdot d+n\cdot d^2))$. The inference complexity $O(T\cdot L\cdot (n^2\cdot d^2+n^2\cdot d+n\cdot d^2))$ for a single sample. The leading term is $n^2\cdot d^2$. which comes from the edge-wise prediction.
• Figure 4: Visualization of graph generation stages across three datasets. Rows correspond to datasets (Comm20, Tree, Planar), and columns correspond to stages (Noise, Coarsened, Expanded).